Multi-objective aerodynamic design exploration for the statically stable shape of the vertical-takeoff-and-landing rocket is conducted through the multi-objective evolutionary computation with the Newtonian method. The Newtonian method is one of the evaluation methods of aerodynamic forces in the supersonic region. Four objective functions are considered; 1)maximization of the lift to drag ratio(L/D) in return flight phase, 2)minimization of the launch drag coefficient(C_{D_Launch}) in ascent phase, 3)maximization of the volume of the body and 4) maximization of the distance from the nose to the center of gravity(x_cg). The maximum-lift-to-drag-ratio and minimum-launch-drag-coefficient shapes are almost the same each other, and they are close to bi-conical shape with small kink angle, similar to the previous study. On the other hand, the shape of the maximum distance from the nose to the center of gravity is found to be a narrow-front-body and wide-aft-body shape. The results also illustrate that the upper limit of the position of the center of gravity, with which the rocket is a statically stable at the angle of attack for the maximum lift-to-drag-ratio,is located at the position of 66% longitudinal length from the top of the body in the shapes considered in this study.